as long as \(f(\Delta ^2)\in \mathbb {B}(L^p(w))\) . For instance, if \(f\)  satisfies [Hormanderconditions]Hormanderconditions with \(s=1\) , then we have \(f(\Delta ^2)\in \mathbb {B}(L^p(w))\)  for any \(w\in A_p\)  and \(1<p<\infty \)  (see Kurtz [1]}). For further results on the weighted boundedness of the Fourier multiplier, we refer to [2]} and references therein.

